More recently, Stein's method has greatly expanded in scope to many distributional types; general univariate [1]}, multivariate [2]}, [3]}, and manifold valued [4]}, [5]}.
One can split Stein's method into two distinct approaches: the classical Stein density approach, and the diffusion approach. In short, the density approach constructs the operator from the density of the target distribution itself, whereas the diffusion approach uses the infinitesimal generator of an over-damped Langevin diffusion.
